Hudson Alexander Loughlin - posted 10:10, Thursday 27 July 2023 - last comment - 12:19, Thursday 27 July 2023(11255)
CMTF Optical Cavity Properties
We're preparing to set up a Pound-Drever-Hall lock to lock a Mephisto laser to a stable, indium optical cavity. The cavity has mirrors labeled "Y1-1037-0-0.50cc" and "PR1-1064-99-IF-1037-UV" the Y1 mirror looks to be a high-reflector with a zero-degrees angle-of-incidence and a 0.5 meter radius of curvature. The PR1 mirror looks to be a flat mirror coated to be 99% reflective at 1064nm on a 1037-UV substrate.
Based on these parameters, we expect the cavity to have a finesse of F = -2*Pi/ln(R1*R2) = 625 where R1 = 1.00 and R2 = 0.99.
The spacing between the mirrors is approximately 255mm and the mirror radii of curvature are r1 = 500mm and r2 = infinity so the cavity stability factor is g = (1 - L/r1)*(1 - L/r2) = (1 - 255/500)*1 = 0.49 so the cavity has a large stability margin. (Cavities are stable as long as 0 < g < 1 and are unstable otherwise.)
Comments related to this report
Since the cavity mode needs to match the radius of curvature at each mirror, we can use the fact that the cavity mode has a waist at the flat mirror and a radius of curvature 1/R(z) = z/(z^2 + zR^2) to calculate the Rayleigh range zR. The waist size is related to the Rayleigh range by zR = pi*w0^2/lambda where lambda = 1064nm is the optical wavelength.
Going through the math, we find that the cavity has a waist size of 291um located at its flat, partially transmissive mirror.